Wreath Product - Canonical Actions of Wreath Products

Canonical Actions of Wreath Products

If the group A acts on a set Λ then there are two canonical ways to construct sets from Ω and Λ on which A WrΩ H (and therefore also A wrΩ H) can act.

  • The imprimitive wreath product action on Λ×Ω.
If ((aω),h)∈A WrΩ H and (λ,ω')∈Λ×Ω, then
.
  • The primitive wreath product action on ΛΩ.
An element in ΛΩ is a sequence (λω) indexed by the H-set Ω. Given an element ((aω), h) ∈ A WrΩ H its operation on (λω)∈ΛΩ is given by
.

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